MathNet 2026 — Part 07 Question 101

Let $\{JOHN\}$ be a rhombus with $JH = 16$ and $ON = 12$. Let $G$ and $P$ be points in $JN$ and $HN$ respectively such that $JG : GN : NP = 2 : 2 : 1$. What is the length $GP$?